From the windows of Diana Balmori’s sixth-storey apartment on Manhattan’s Upper West Side, the treetops of Central Park look close enough to touch, separated by little more than a street and a low wall. But it is this very separation that Balmori’s career in landscape design – culminating in Balmori Associates, the Manhattan-based firm she runs – has sought to erase

The 19th-century park, she says, represents an outdated idea of how cities – and their inhabitants – relate to nature: “You wall it [off] as much as possible to say, we are totally distinct from that stuff that’s out there.”

Balmori aims to “put the city in nature rather than putting nature in the city ... you make the whole city work according to how nature works. But it doesn’t mean that you have to plonk some trees in it.”

Sitting in a sleek tan armchair in her sun-filled living room, Balmori gestures to illustrate her point. You get the sense she would be just as comfortable drawing her ideas on the sketchpad propped near the window as she is setting them out in words.

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Drawing is her preferred method of taking notes, though a camera will do when she doesn’t have a notebook at hand. “You become very quiet and still inside when you’re drawing, and you see so much more than you see with a camera,” she says. “I use it as an instrument for seeing.”

The living room, with its large windows, blond wood floor, checkerboard rug and black marble fireplace, is an ideal place for quiet sketching but also serves as a stage for the music and dance performances she loves to host. The open, lightly furnished space is complemented by the dining room next door, where a large table is framed by floor-to-ceiling bookshelves, several dedicated to Balmori’s collection of dictionaries and to objects she has collected on her travels: animal figurines from Mexico and Argentina, a Chinese scholar stone, a smooth, ostrich egg-sized rock she plucked from a river in Maine.

When she bought the spacious two-bedroom apartment seven years ago, she says, “I tried to simplify everything”. White walls, hung with friends’ photography and drawings, are set off by doorframes from which Balmori has stripped the paint, revealing a deep, silvery steel. The kitchen cabinets have received the same treatment, their metallic coolness contrasting with a tall wood table.

Balmori has been at home among artists from a young age. Her mother filled the house with fellow musicians and painters – first in Spain, where Balmori was born, then her mother’s native England, and finally Argentina, where her linguist father studied indigenous languages.

“The changing of countries and changing of languages I think is something that defines our time,” she says. “Nearly everybody has had to do this in this century and it’s a different way of seeing the world.”

Balmori’s vision of a world in which people, buildings, infrastructure and nature are woven together is laid out in her aptly titled A Landscape Manifesto but comes alive in the work of her landscape and urban design company. She has spent more than a decade remaking the old industrial port of Bilbao, Spain. Undulating parks connect cultural landmarks such as Frank Gehry’s Guggenheim and the Teatro Arriaga with downtown, incorporating a light railway line and paths for walking, jogging and cycling along the Nervión river.

In New Haven, Connecticut – home of Yale University, where she has taught landscape history and architecture since the 1990s – Balmori worked with the community to transform 14 miles of an old railroad track into a linear park that runs into the heart of the city.

Her latest project is a section of the new South Korean city of Sejong. Low office buildings are linked by a park that drapes across their roofs like a vast blanket. Balmori has been a longtime advocate of “green roofs” – rooftops planted with vegetation. This shared space offers environmental benefits – moderating temperatures, absorbing rainwater and providing insulation – while also serving as a pedestrian path between buildings.

The idea that public spaces should play a range of roles runs through Balmori’s work. She is fluent in urban design, having studied architecture as an undergraduate in Argentina and completed a PhD in urban history at UCLA. After teaching at the State University of New York at Oswego from 1974 to 1981, she decided it would be more interesting to design rather than simply write about landscape.

She left academia in 1981 and joined the architecture firm César Pelli, where she launched a landscape practice, and then struck out on her own with Balmori Associates in 1990.

A Landscape Manifesto, published in 2010, distils the principles that Balmori developed and applied during the previous two decades, including embracing the fluidity of nature, deriving form from natural systems and shedding nostalgia.

“You just can’t pick up what was done in the Renaissance or in the 18th century and plonk it in the 21st century, because it was answering questions that we don’t have now.

“For the most part each one [of the projects in the book] had some sort of important lesson that could be thought of as a general idea, useful to our time. And what I felt valuable about it was ... it wasn’t something that had been done in the past or that should be done in the future, but really that it responds to the conditions that we’re working in now and how we see the world now.”

She says landscape design, with its current emphasis on ecology and engineering, is ideally suited to address the questions raised by modern cities – how we affect the climate, how we deal with waste, how we can make infrastructure more sustainable and resilient.

“Suddenly the set of ideas that landscape is working with is much more interesting than the set of ideas in architecture today; they just fit the time.”

The perils of a changing climate were all too clear in October, when superstorm Sandy hammered the east coast of the US, killing more than 100 people in several states, causing billions of dollars of devastation and leaving areas of New York City in darkness for weeks.

While Balmori’s home was unscathed, she got an up-close look at the flooding from her downtown studio, which sits just a block from the Hudson river in an area where the storm surge topped 17ft.

“The west side was just incredible; water, water, water,” she says. Her office lost power for two weeks but was spared greater damage.

As the region deliberates over longer-term rebuilding, Balmori takes a sceptical view of calls for sea walls or flood barriers across the harbour.

“I think that we have the tools for doing a lot of modest, small things, and not attacking this problem by saying we have to change the whole infrastructure,” she says. “I think that’s a 19th-century approach.”

She suggests measures such as restoring “soft” edges to the city, such as marshes and oyster beds that could absorb some of the water and allow it to flow rather than flooding residential neighbourhoods.

“[Politicians and city planners] have to address climate change, they just have to,” she says. “If they don’t address the issue then it’s money wasted. A surge barrier does not address the issue, it’s not doing anything about climate change, it’s just trying to protect us against the next attack. But why can’t we try to diminish the attacks that we’re going to get from the weather, and from what we’re doing in general over the whole planet?”

Also on her mind are those green roofs, which can help reduce the urban heat island effect – where concrete and buildings make a city warmer than its surrounding suburbs and rural areas – endemic to places like Manhattan.

“Make all the roofs green in New York City and we would have a real effect on climate change,” she says.

Balmori points out a simple sketch in reddish tones propped on a ledge in the hallway. It’s a portrait of her mother by Argentine artist Héctor Cartier.

Balmori speaks admiringly of her mother, an accomplished musician who attended Cambridge university in the 1920s before it granted degrees to women. She hoped her daughter would follow her path to university in England but, Balmori says, “I was very interested in the States and I felt that that was the old world ... I should have listened to her but you are very stubborn when you’re growing up. You think you know everything.”

She smiles as she traces the lines of the portrait’s faintly defined features with her finger. “It has that kind of mysterious quality that my mother had, and I think it sort of captures her character in some way because it leaves lots to the imagination.”